Number of 5 Card Hold'em Boards with No Str8 or Flush is Possible? - Gambling and Probability

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Number of 5 Card Hold'em Boards with No Str8 or Flush is Possible?

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03-28-2015 , 09:59 PM

R Gibert

adept

Join Date: Jan 2006 Posts: 936

Not considering your own hand, how many 5 card Hold'em boards are there with no str8 or flush being possible?
Considering your own hand, what starting hand would minimize the number of possible boards with no str8 or flush?
...And what starting hand would maximize their number?

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03-28-2015 , 10:26 PM

goktrenks

adept

Join Date: Jul 2014 Posts: 855

I can't answer the 1st or 2nd question but about 3rd I think JT is the hand that makes more nut straights possible

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03-29-2015 , 01:40 AM

whosnext

Carpal \'Tunnel

Join Date: Mar 2009 Posts: 6,730

I wrote a quick and dirty program to answer #1 to tabulate the number of five-card boards for which there are no straight or flush possibilities by the following board categories:

624 four of a kind + one singleton

3,744 three of a kind + one pair

34,788 three of a kind + two singletons

72,252 two pair + one singleton

291,312 one pair + three singletons

55,800 five singletons

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458,520 GRAND TOTAL

I will attempt to confirm these answers in due course, but others are encouraged to confirm/deny them since I am not 100% sure of their veracity.

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03-29-2015 , 02:34 AM

heehaww

Pooh-Bah

Join Date: Aug 2011 Posts: 5,081

#2 guess = K2 suited

#3 guess = T5 off

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03-29-2015 , 05:25 AM

Buzz

gramps

Join Date: Sep 2002 Posts: 18,254

Quote:

Originally Posted by R Gibert

Not considering your own hand, how many 5 card Hold'em boards are there with no str8 or flush being possible?

As an Omaha and Omaha-8 player, I'm interested in how often the board doesn't enable a straight or better.

Without consideration for your own cards, I think there are 79*600=47,400 unpaired boards that enable neither straights nor flushes. (Took me hours to compute and tabulate that).

(As an Omaha and Omaha-8 player, I'm not interested in how many paired boards don't enable straights or flushes, since paired boards enable quads and full houses).

Buzz

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03-29-2015 , 08:44 AM

heehaww

Pooh-Bah

Join Date: Aug 2011 Posts: 5,081

Quote:

Originally Posted by heehaww

#2 guess = K2 suited

I change my mind, now I think it's a tie between 32 and KQ.

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